Lesson Worksheet: Acoustic Impedance Physics

In this worksheet, we will practice describing the use of reflected sound waves from boundaries of media of varying acoustic impedances to measure densities and propagation speeds.

Q1:

The acoustic impedance of some muscle tissue is 1.70 kg/m2⋅s, and the acoustic impedance of some bone in contact with the muscle is 7.80 kg/m2⋅s. Sound waves travel through the muscle, are incident on the bone surface, and reflect from it. Find the ratio of the reflected sound wave intensity to the incident sound intensity. Answer to two decimal places.

Q2:

Which of the following formulas correctly relates 𝑐, the speed of sound in a medium, 𝜌, the density of a medium, and 𝑍, the acoustic impedance of a medium?

  • A𝑍=(𝜌𝑐)
  • B𝑍=𝜌𝑐
  • C𝑍=(𝜌𝑐)
  • D𝑍=𝑐𝜌
  • E𝑍=𝜌𝑐

Q3:

Ultrasonic-frequency sound waves are used in medical imaging. Ultrasonic emitters are placed in contact with irregularly shaped body parts, leaving small air gaps between the emitter and the body part. Which of the following correctly explains why using ultrasonic frequency sound waves to measure reflected sound from body parts requires a coupling medium between the source of the sound waves and the body parts?

  • AAir in air gaps will change the frequency of the sound waves to lower-than-ultrasonic frequencies.
  • BAir in air gaps will strongly scatter sound waves.
  • CThe acoustic impedances of air and body tissues are sufficiently different that only a very small fraction of sound wave intensity is transmitted.
  • DThe acoustic impedances of air and body tissues are sufficiently different that only a very small fraction of sound wave intensity is reflected.
  • EThe coupling medium deforms the surface of the body parts so that they are regularly shaped.

Q4:

Two substances, substance A and substance B, have acoustic impedances of 𝑍 and 𝑍 respectively. The substances meet at a boundary. The intensity of sound waves propagating in substance A before arriving at the boundary is 𝐼, and the intensity of sound waves propagating in substance A after reflecting from the boundary is 𝐼. Which of the following formulas correctly relates 𝑍, 𝑍, 𝐼, and 𝐼?

  • A𝐼𝐼=(𝑍𝑍)(𝑍+𝑍)
  • B𝐼𝐼=(𝑍+𝑍)(𝑍𝑍)
  • C𝐼𝐼=𝑍+𝑍𝑍𝑍
  • D𝐼𝐼=𝑍𝑍𝑍+𝑍
  • E𝐼𝐼=𝑍𝑍𝑍+𝑍

Q5:

Sound waves propagate in a sheet of metal at 4,660 m/s. The density of the metal is 8,930 kg/m3. Find the acoustic impedance of the metal. Answer in scientific notation to two decimal places.

  • A9.36×10 kg/m2⋅s
  • B3.06×10 kg/m2⋅s
  • C1.36×10 kg/m2⋅s
  • D4.16×10 kg/m2⋅s
  • E1.82×10 kg/m2⋅s

Q6:

Sound waves propagate in a liquid at 1,570 m/s. The acoustic impedance of the liquid is 1.63×10 kg/m2⋅s. Find the density of the liquid. Answer in scientific notation to two decimal places.

  • A1.14×10 kg/m3
  • B1.60×10 kg/m3
  • C9.63×10 kg/m3
  • D1.32×10 kg/m3
  • E1.04×10 kg/m3

Q7:

The acoustic impedance of some fat tissue is 1.38×10 kg/m2⋅s, and that of some muscle tissue in contact with the fat is 1.72×10 kg/m2⋅s. Sound waves travel through the muscle, are incident on the fat surface, and reflect from it. Find the ratio of the transmitted sound wave intensity to the incident sound intensity. Answer to three decimal places.

Q8:

Substance A has a density 𝜌A and substance B has a density 𝜌B, where 𝜌=2𝜌AB. The speeds at which sound waves propagate in substance A and substance B are 𝑐A and 𝑐B, respectively, where 𝑐=3𝑐AB. Sound waves incident at a boundary between the substances are reflected. Find the ratio of the reflected wave intensity to the incident wave intensity. Answer to two decimal places.

Q9:

A solid object has an acoustic impedance of 7.8×10 kg/m2⋅s. The density of the object is 1,850 kg/m3. Find the speed at which sound waves propagate in the object. Answer to the nearest meter per second.

Q10:

Two substances, substance A and substance B, have acoustic impedances of 𝑍 and 𝑍, respectively, where 𝑍=1.2/kgms. The substances meet at a boundary. The intensity of sound waves propagating in substance A before arriving at the boundary is 𝐼 and after reflecting from the boundary is 𝐼. The ratio of 𝐼 to 𝐼 is 0.42. Find 𝑍. Answer to two decimal places.

This lesson includes 24 additional question variations for subscribers.

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